The US president, George Bush, and his Russian counterpart, Vladimir Putin, moved yesterday towards a surprise compromise over Washington's plan to build a new missile defence shield and scrap the 1972 anti-ballistic missile treaty.

The two agreed to tie the national missile defence system (NMD) to a reduction in their stockpiles of offensive strategic missiles.

Mr Putin has regularly expressed hostility towards NMD and warned that unilateral abandonment by the US of the ABM treaty, which helped to maintain peace during the cold war, could begin another arms race.

Mr Bush, who met Mr Putin in Genoa after the G8 summit ended, has said repeatedly that the missile shield is intended for protection not against Russia but against "rogue" states such as North Korea and Iraq.

Mr Putin said Mr Bush's offer to tie NMD to offensive weapons was unexpected and he was not ready at this stage to talk about how much stockpiles might be reduced. "But a joint striving exists," he said.

Mr Putin has suggested in the past that 1,500 strategic missiles each, or even less, would be a sufficient arsenal for each side. The US has 7,000 at present.

Most European countries, particularly France, have openly criticised Mr Bush for pushing ahead with the missile programme and for threatening to scrap the ABM treaty. But the prime minister, Tony Blair, anxious not to offend Mr Bush, said the best approach was to wait and see whether the missile plan proved practical and whether Mr Bush and Mr Putin could reach a compromise on the ABM treaty.

The US-Russian statement said: "We agreed that major changes in the world require concrete discussions of both offensive and defensive systems. We already have some strong and tangible points of agreement. We will shortly begin intensive consultations on the interrelated subjects of offensive and defensive systems."

Mr Bush, at a press conference after their talks, said: "We have agreed to find common ground if possible. I believe we'll come up with an accord. We'll work hard toward one."

Mr Bush suggested it might be possible, by way of compromise, to meet Mr Putin's objections to the scrapping of the ABM treaty by negotiating a new treaty.

He described himself and Mr Putin as "young leaders who are interested in forging a more peaceful world".

After they first met in Slovenia last month, Mr Bush said the meeting had been cordial, but Mr Putin later criticised Mr Bush over the missile plan.

Mr Putin threatened that if the US abandoned the ABM treaty, Russia would consider all other nuclear weapons treaties to be void too.

He has also suggested that Moscow could fit multiple warheads to its single warhead missiles, a dangerous form of escalation.

Asked about that threat yesterday, Mr Putin said that if the new talks went well, "we might not ever need to look at that option, but it's one of our options".